Christina Zarb

activity

20142026

most citedEquating two maximum degrees

4 citations · 11 across the 17 of their papers we have counts for

collaborators

22 papers

math.CO2026

Spreads of degrees in maximal planar graphs -- an exposition

Yair Caro, Riste Škrekovski, Christina Zarb

For a graph $G$ and a set $B \subseteq V (G)$ , the spread $sp (B)$ of $B$ is the difference between the largest and the smallest degree in $G$ of a vertex of $B$ , and for an…

math.CO2026

Spreads of degrees in graphs

Yair Caro, Riste Škrekovski, Christina Zarb

For a graph $G$ and a set $B \subseteq V (G)$ , the spread $sp (B)$ of $B$ is the difference between the largest and the smallest degree in $G$ of a vertex of $B$ , and for an…

math.CO2026

Induced/Incomparable versus Ramsey

Yair Caro, Zsolt Tuza, Christina Zarb

We consider the following problem: Let $H$ and $F$ be two graphs on $k$ vertices and assume $F \neq = H$ . We say that $H$ and $F$ are incomparable if neither $F$ nor $H$ contains the…

math.CO2023★ 1 cited

Flip colouring of graphs

Yair Caro, Josef Lauri, Xandru Mifsud +2

It is proved that for integers $b, r$ such that $3 \leq b < r \leq (2 b + 1) - 1$ , there exists a red/blue edge-colored graph such that the red degree of every vertex is $r$ ,…

math.CO2023

The Feasibility Problem -- the family $F$ $(G)$ of all induced $G$ -free graphs

Yair Caro, Matthew Cassar, Josef Lauri +1

An infinite family of graphs $F$ is called feasible if for any pair of integers $(n, m)$ , $n \geq 1$ , $0 \leq m \leq (2 n)$ , there is a member $G \in F$ such th…

math.CO2021

The feasibility problem for line graphs

Yair Caro, Josef Lauri, Christina Zarb

We consider the following feasibility problem: given an integer $n \geq 1$ and an integer $m$ such that $0 \leq m \leq (2 n)$ , does there exist a line graph $L = L (G)$ with…

math.CO2021

Index of Parameters of Iterated Line Graphs

Yair Caro, Josef Lauri, Christina Zarb

Let $G$ be a prolific graph, that is a finite connected simple graph which is not isomorphic to a cycle nor a path nor the star graph $K_{1, 3}$ . The line-graph of $G$ , denoted by $…

math.CO2020

On zero-sum spanning trees and zero-sum connectivity

Yair Caro, Adriana Hansberg, Josef Lauri +1

We consider $2$ -colourings $f : E (G) \to {- 1, 1}$ of the edges of a graph $G$ with colours $- 1$ and $1$ in $Z$ . A subgraph $H$ of $G$ is said to be a zero-sum…

math.CO2019

A note on totally-omnitonal graphs

Yair Caro, Josef Lauri, Christina Zarb

Let the edges of the complete graph $K_{n}$ be coloured red or blue, and let $G$ be a graph with $∣ V (G) ∣ < n$ . Then ot(n,G) is defined to be the minimum integer, if it exists, such t…

math.CO2019

On small balanceable, strongly-balanceable and omnitonal graphs

Yair Caro, Josef Lauri, Christina Zarb

In Ramsey theory for graphs we are given a graph $G$ and we are required to find the least $n_{0}$ such that, for any $n \geq n_{0}$ , any red/blue colouring of the edges of $K_{n}$ gives…

math.CO2018

Notes on Spreads of Degrees in Graphs

Yair Caro, Josef Lauri, Christina Zarb

Perhaps the very first elementary exercise one encounters in graph theory is the result that any graph on at least two vertices must have at least two vertices with the same degree…

math.CO2017★ 4 cited

Equating two maximum degrees

Yair Caro, Josef Lauri, Christina Zarb

Given a graph $G$ , we would like to find (if it exists) the largest induced subgraph $H$ in which there are at least $k$ vertices realizing the maximum degree of $H$ . This problem…

math.CO2016

Two short proofs of the Perfect Forest Theorem

Yair Caro, Josef Lauri, Christina Zarb

A perfect forest is a spanning forest of a connected graph $G$ , all of whose components are induced subgraphs of $G$ and such that all vertices have odd degree in the forest. A per…

math.CO2015★ 1 cited

Selective Hypergraph Colourings

Yair Caro, Josef Lauri, Christina Zarb

We look at colourings of $r$ -uniform hypergraphs, focusing our attention on unique colourability and gaps in the chromatic spectrum. The pattern of an edge $E$ in an $r$ -uniform hy…

math.CO2015

Ramsey numbers for degree monotone paths

Yair Caro, Raphael Yuster, Christina Zarb

A path $v_{1}, v_{2}, \dots, v_{m}$ in a graph $G$ is $d e g r ee$ - $m o n o t o n e$ if $d e g (v_{1}) \leq d e g (v_{2}) \leq \dots \leq d e g (v_{m})$ where $d e g (v_{i})$ is the degree of $v_{i}$ in $G$ . Longest degr…

math.CO2014

The Saturation Number for the length of Degree Monotone Paths

Yair Caro, Josef Lauri, Christina Zarb

A degree monotone path in a graph $G$ is a path $P$ such that the sequence of degrees of the vertices in the order in which they appear on $P$ is monotonic. The length of the longe…

math.CO2014★ 1 cited

Degree Monotone Paths and Graph Operations

Yair Caro, Josef Lauri, Christina Zarb

A path $P$ in a graph $G$ is said to be a degree monotone path if the sequence of degrees of the vertices of $P$ in the order in which they appear on $P$ is monotonic. The length o…

math.CO2014

Hamiltonicity and $σ$ -hypergraphs

Christina Zarb

We define and study a special type of hypergraph. A $σ$ -hypergraph $H = H (n, r, q$ $∣$ $σ$ ), where $σ$ is a partition of $r$ , is an $r$ -uniform hypergraph having $n q$ vertices part…

math.CO2014★ 3 cited

Degree Monotone Paths

Yair Caro, Josef Lauri, Christina Zarb

We shall study degree-monotone paths in graphs, a problem inspired by the celebrated theorem of Erd{ő}s-Szekeres concerning the longest monotone subsequence of a given sequence of…

math.CO2014★ 1 cited

Independence and Matchings in $σ$ -hypergraphs

Yair Caro, Josef Lauri, Christina Zarb

Let $σ$ be a partition of the positive integer $r$ . A $σ$ -hypergraph $H = H (n, r, q ∣ σ)$ is an $r$ -uniform hypergraph on $n q$ vertices which are partitioned into $n$ classes $V_1, V_2,…

math.CO2014

$(2, 2)$ -colourings and clique-free $σ$ -hypergraphs

Yair Caro, Josef Lauri, Christina Zarb

We consider vertex colourings of $r$ -uniform hypergraphs $H$ in the classical sense, that is such that no edge has all its vertices given the same colour, and $(2, 2)$ -colourings of…

math.CO2014

Constrained colouring and $σ$ -hypergraphs

Yair Caro, Josef Lauri, Christina Zarb

A constrained colouring or, more specifically, an $(α, β)$ -colouring of a hypergraph $H$ , is an assignment of colours to its vertices such that no edge of $H$ contains less than $α$ …

Spreads of degrees in maximal planar graphs -- an exposition

Spreads of degrees in graphs

Induced/Incomparable versus Ramsey

Flip colouring of graphs

The Feasibility Problem -- the family F(G) of all induced G-free graphs

The feasibility problem for line graphs

Index of Parameters of Iterated Line Graphs

On zero-sum spanning trees and zero-sum connectivity

A note on totally-omnitonal graphs

On small balanceable, strongly-balanceable and omnitonal graphs

Notes on Spreads of Degrees in Graphs

Equating two maximum degrees

Two short proofs of the Perfect Forest Theorem

Selective Hypergraph Colourings

Ramsey numbers for degree monotone paths

The Saturation Number for the length of Degree Monotone Paths

Degree Monotone Paths and Graph Operations

Hamiltonicity and σ-hypergraphs

Degree Monotone Paths

Independence and Matchings in σ-hypergraphs

(2,2)-colourings and clique-free σ-hypergraphs

Constrained colouring and σ-hypergraphs

The Feasibility Problem -- the family $F$ $(G)$ of all induced $G$ -free graphs

Hamiltonicity and $σ$ -hypergraphs

Independence and Matchings in $σ$ -hypergraphs

$(2, 2)$ -colourings and clique-free $σ$ -hypergraphs

Constrained colouring and $σ$ -hypergraphs